{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "isolated-intervention",
   "metadata": {},
   "source": [
    "## 习题 3.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "deadly-young",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 4 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>催化剂</th><th scope=col>X.产品得率1</th><th scope=col>X.产品得率2</th><th scope=col>X.产品得率3</th><th scope=col>X.产品得率4</th><th scope=col>X.产品得率5</th><th scope=col>X.产品得率6</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>A1</td><td>0.88</td><td>0.85</td><td>0.79</td><td>0.86</td><td>0.85</td><td>0.83</td></tr>\n",
       "\t<tr><td>A2</td><td>0.87</td><td>0.92</td><td>0.85</td><td>0.83</td><td>0.90</td><td>0.80</td></tr>\n",
       "\t<tr><td>A3</td><td>0.84</td><td>0.78</td><td>0.81</td><td>0.80</td><td>0.85</td><td>0.83</td></tr>\n",
       "\t<tr><td>A4</td><td>0.81</td><td>0.86</td><td>0.90</td><td>0.87</td><td>0.78</td><td>0.79</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 4 × 7\n",
       "\\begin{tabular}{lllllll}\n",
       " 催化剂 & X.产品得率1 & X.产品得率2 & X.产品得率3 & X.产品得率4 & X.产品得率5 & X.产品得率6\\\\\n",
       " <chr> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t A1 & 0.88 & 0.85 & 0.79 & 0.86 & 0.85 & 0.83\\\\\n",
       "\t A2 & 0.87 & 0.92 & 0.85 & 0.83 & 0.90 & 0.80\\\\\n",
       "\t A3 & 0.84 & 0.78 & 0.81 & 0.80 & 0.85 & 0.83\\\\\n",
       "\t A4 & 0.81 & 0.86 & 0.90 & 0.87 & 0.78 & 0.79\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 4 × 7\n",
       "\n",
       "| 催化剂 &lt;chr&gt; | X.产品得率1 &lt;dbl&gt; | X.产品得率2 &lt;dbl&gt; | X.产品得率3 &lt;dbl&gt; | X.产品得率4 &lt;dbl&gt; | X.产品得率5 &lt;dbl&gt; | X.产品得率6 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| A1 | 0.88 | 0.85 | 0.79 | 0.86 | 0.85 | 0.83 |\n",
       "| A2 | 0.87 | 0.92 | 0.85 | 0.83 | 0.90 | 0.80 |\n",
       "| A3 | 0.84 | 0.78 | 0.81 | 0.80 | 0.85 | 0.83 |\n",
       "| A4 | 0.81 | 0.86 | 0.90 | 0.87 | 0.78 | 0.79 |\n",
       "\n"
      ],
      "text/plain": [
       "  \\u50ac\\u5316\\u5242 X.\\u4ea7\\u54c1\\u5f97\\u73871 X.\\u4ea7\\u54c1\\u5f97\\u73872\n",
       "1 A1                 0.88                        0.85                       \n",
       "2 A2                 0.87                        0.92                       \n",
       "3 A3                 0.84                        0.78                       \n",
       "4 A4                 0.81                        0.86                       \n",
       "  X.\\u4ea7\\u54c1\\u5f97\\u73873 X.\\u4ea7\\u54c1\\u5f97\\u73874\n",
       "1 0.79                        0.86                       \n",
       "2 0.85                        0.83                       \n",
       "3 0.81                        0.80                       \n",
       "4 0.90                        0.87                       \n",
       "  X.\\u4ea7\\u54c1\\u5f97\\u73875 X.\\u4ea7\\u54c1\\u5f97\\u73876\n",
       "1 0.85                        0.83                       \n",
       "2 0.90                        0.80                       \n",
       "3 0.85                        0.83                       \n",
       "4 0.78                        0.79                       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "raw_data <- read.csv(\"./ex_3_4.csv\")\n",
    "raw_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stock-recommendation",
   "metadata": {},
   "source": [
    "为方便后续分析，先将数据处理成 $<A, x>$ 的序对形式："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dedicated-valuation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 24 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>A</th><th scope=col>x</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>A1</td><td>0.88</td></tr>\n",
       "\t<tr><td>A1</td><td>0.85</td></tr>\n",
       "\t<tr><td>A1</td><td>0.79</td></tr>\n",
       "\t<tr><td>A1</td><td>0.86</td></tr>\n",
       "\t<tr><td>A1</td><td>0.85</td></tr>\n",
       "\t<tr><td>A1</td><td>0.83</td></tr>\n",
       "\t<tr><td>A2</td><td>0.87</td></tr>\n",
       "\t<tr><td>A2</td><td>0.92</td></tr>\n",
       "\t<tr><td>A2</td><td>0.85</td></tr>\n",
       "\t<tr><td>A2</td><td>0.83</td></tr>\n",
       "\t<tr><td>A2</td><td>0.90</td></tr>\n",
       "\t<tr><td>A2</td><td>0.80</td></tr>\n",
       "\t<tr><td>A3</td><td>0.84</td></tr>\n",
       "\t<tr><td>A3</td><td>0.78</td></tr>\n",
       "\t<tr><td>A3</td><td>0.81</td></tr>\n",
       "\t<tr><td>A3</td><td>0.80</td></tr>\n",
       "\t<tr><td>A3</td><td>0.85</td></tr>\n",
       "\t<tr><td>A3</td><td>0.83</td></tr>\n",
       "\t<tr><td>A4</td><td>0.81</td></tr>\n",
       "\t<tr><td>A4</td><td>0.86</td></tr>\n",
       "\t<tr><td>A4</td><td>0.90</td></tr>\n",
       "\t<tr><td>A4</td><td>0.87</td></tr>\n",
       "\t<tr><td>A4</td><td>0.78</td></tr>\n",
       "\t<tr><td>A4</td><td>0.79</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 24 × 2\n",
       "\\begin{tabular}{ll}\n",
       " A & x\\\\\n",
       " <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t A1 & 0.88\\\\\n",
       "\t A1 & 0.85\\\\\n",
       "\t A1 & 0.79\\\\\n",
       "\t A1 & 0.86\\\\\n",
       "\t A1 & 0.85\\\\\n",
       "\t A1 & 0.83\\\\\n",
       "\t A2 & 0.87\\\\\n",
       "\t A2 & 0.92\\\\\n",
       "\t A2 & 0.85\\\\\n",
       "\t A2 & 0.83\\\\\n",
       "\t A2 & 0.90\\\\\n",
       "\t A2 & 0.80\\\\\n",
       "\t A3 & 0.84\\\\\n",
       "\t A3 & 0.78\\\\\n",
       "\t A3 & 0.81\\\\\n",
       "\t A3 & 0.80\\\\\n",
       "\t A3 & 0.85\\\\\n",
       "\t A3 & 0.83\\\\\n",
       "\t A4 & 0.81\\\\\n",
       "\t A4 & 0.86\\\\\n",
       "\t A4 & 0.90\\\\\n",
       "\t A4 & 0.87\\\\\n",
       "\t A4 & 0.78\\\\\n",
       "\t A4 & 0.79\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 24 × 2\n",
       "\n",
       "| A &lt;chr&gt; | x &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| A1 | 0.88 |\n",
       "| A1 | 0.85 |\n",
       "| A1 | 0.79 |\n",
       "| A1 | 0.86 |\n",
       "| A1 | 0.85 |\n",
       "| A1 | 0.83 |\n",
       "| A2 | 0.87 |\n",
       "| A2 | 0.92 |\n",
       "| A2 | 0.85 |\n",
       "| A2 | 0.83 |\n",
       "| A2 | 0.90 |\n",
       "| A2 | 0.80 |\n",
       "| A3 | 0.84 |\n",
       "| A3 | 0.78 |\n",
       "| A3 | 0.81 |\n",
       "| A3 | 0.80 |\n",
       "| A3 | 0.85 |\n",
       "| A3 | 0.83 |\n",
       "| A4 | 0.81 |\n",
       "| A4 | 0.86 |\n",
       "| A4 | 0.90 |\n",
       "| A4 | 0.87 |\n",
       "| A4 | 0.78 |\n",
       "| A4 | 0.79 |\n",
       "\n"
      ],
      "text/plain": [
       "   A  x   \n",
       "1  A1 0.88\n",
       "2  A1 0.85\n",
       "3  A1 0.79\n",
       "4  A1 0.86\n",
       "5  A1 0.85\n",
       "6  A1 0.83\n",
       "7  A2 0.87\n",
       "8  A2 0.92\n",
       "9  A2 0.85\n",
       "10 A2 0.83\n",
       "11 A2 0.90\n",
       "12 A2 0.80\n",
       "13 A3 0.84\n",
       "14 A3 0.78\n",
       "15 A3 0.81\n",
       "16 A3 0.80\n",
       "17 A3 0.85\n",
       "18 A3 0.83\n",
       "19 A4 0.81\n",
       "20 A4 0.86\n",
       "21 A4 0.90\n",
       "22 A4 0.87\n",
       "23 A4 0.78\n",
       "24 A4 0.79"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = c()\n",
    "x = c()\n",
    "for (row in 1:nrow(raw_data)) {\n",
    "    for (col in 2:ncol(raw_data)) {\n",
    "        A = c(A, raw_data[row, 1])\n",
    "        x = c(x, raw_data[row, col])\n",
    "    }\n",
    "}\n",
    "data = data.frame(A, x)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fallen-simon",
   "metadata": {},
   "source": [
    "### 正态性检验\n",
    "\n",
    "首先，第一步，需要对数据进行正态性检验：\n",
    "\n",
    "用 `shapiro.test` 检验 4 组数据是否服从正态分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "previous-mistress",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  x[1:6]\n",
       "W = 0.92835, p-value = 0.5674\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  x[7:12]\n",
       "W = 0.9831, p-value = 0.9659\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  x[13:18]\n",
       "W = 0.96579, p-value = 0.8631\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  x[19:24]\n",
       "W = 0.92097, p-value = 0.5124\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(x[1:6])\n",
    "shapiro.test(x[7:12])\n",
    "shapiro.test(x[13:18])\n",
    "shapiro.test(x[19:24 ])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "divine-house",
   "metadata": {},
   "source": [
    "A1、A2、A3、A4 四个组的 shapiro.test 检验 p 值依次为 0.5674、0.9659、0.8631、0.5124，均大于 0.05，\n",
    "认为原假设成立（$H_0$：假设数据服从正态分布），表明 4 组数据均来自正态分布总体。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "joined-bermuda",
   "metadata": {},
   "source": [
    "### 方差齐次检验\n",
    "\n",
    "接下来进行方差齐次检验：\n",
    "\n",
    "用 `bartlett.test` 检验 4 个分组数据方差是否一致："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "incomplete-paintball",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tBartlett test of homogeneity of variances\n",
       "\n",
       "data:  x by A\n",
       "Bartlett's K-squared = 2.2257, df = 3, p-value = 0.5269\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bartlett.test(x ~ A, data = data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "narrow-rugby",
   "metadata": {},
   "source": [
    "得到 p-value = 0.5269 > 0.05，认为原假设成立（$H_0$：假设 4 组数据方差相等），表明 4 组数据的方差齐次。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "latin-administration",
   "metadata": {},
   "source": [
    "通过了上面两个检验，下面就可以开始做单因素方差分析了。\n",
    "\n",
    "### 图形可视化\n",
    "\n",
    "开始之前，还可以考虑先用箱图观察一下几组数据的分布："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "identified-papua",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+vD87hWtZvd6nK7hyb/NnvjZtyvwvNJ\nyVYDvvZRA+5nNwIExiewew79u+M7/MxOvWPX9ynH1epHta8Y18EdlwABAgQIjEKg6wXSuUGs\n1elOSl6V1Bmjag9M/uruezMz5/dud8jtnyS7JF/vbdvcm9/IC/8uqdONg7QqzKr1b+955H8J\nEJgkgZemM28cY4f6/z2pRWfG1d6dA79tXAd3XAIECBAgQGD5AlUA/ktSl9jV7x19qZdre9uq\niOm3y3Kn9vtO0v9DpP/csG9rpb069vwzWsM+rvcnQGB6BE5OVysaAQIECBCYNIH627n+lq3v\n1U99q0vButzqsrpDkvckdXbmqb3U7yHV2aKjk377Ru68PXliMs5/oe33xy0BAgQIECBAgAAB\nAiMW6PoldsX5i+QNvTw4t7VKXZ1Nmt+eO3+DxwQIECBAgAABAgQItCXQQoE0e0brR2I1AgQI\nECBAgAABAgQILCjQ9UvsFhz0IhtfkedqWfCXL7KPpwgQIECAAAECBAgQ6KiAAmnuxO6ah/sk\ndasRIECAAAECBAgQINCYQGuX2G1qej+aHT6XXLmpHT1PgACBEQucPuLjORwBAgQIEGhSQIE0\nd9qrMFIczTXxiACByRA4azK6oRcECBAgQKDbAi0WSDtmSutHYbdJbkquS/o/IJu7GgECBAgQ\nIECAAAECrQq08h2kfTPBn0yuStYlq5OLk7VJFUk/Tk5Kdk40AgQIECBAgAABAgQaFWjhDNLx\nmdtVvfldk9sLkyqSqjCqM0k7JXsmxyX1W0ivSk5LNAIECBAgQIAAAQIECHRK4IiM5q7kS8lj\nFxnZFnnu4OSbSe1/YDLKdmwOVsfdbpQHdSwCBAgQIECAAAECKyCwdd6j/pZ9wgq8l7cYssCp\nef+6fK6+bzRIq+8n3ZB8bJCdV3AfBdIKYnorAh0VeFvG1T8b3tEhGhYBAgQITKlApwqkrl9i\nt08+ZHVJ3W0DftiuzX4XJXsMuL/dCBAgMCqBuhRYI0CAAAECBIYs0PVFGn4av/2SrQZ0rDNI\nVVTVAg4aAQIECBAgQIAAAQKNCXS9QDol87l3ckZywCJzW99BOig5J7lf8oVEI0CAAAECBAgQ\nIECgMYGuX2JXq9HtkpyYHJZcnqxNrknqu0bbJzsleyW7JeuT1yUXJBoBAgQIECBAgAABAgQ6\nKfDwjOozSRVItcLG7NSPxP578t7kock42rE5aPXJKnbj0HdMAtMhcHK6WdEIECBAgMCkCVik\nYdJmZID+XJJ9jurtV2eN6vePtk3qh2OvTzQCBAgQIECAAAECBAjMdP0Su4WmuC6tq2gECBCY\nJoE16WydadYIECBAgACBIQq0WCANkdNbEyBAYGgCxw/tnb0xAQIECBAg8CuBrq9i96uBukOA\nAAECBAgQIECAAIFNCSiQNiXkeQIECBAgQIAAAQIEmhFQIDUz1QZKgAABAgQIECBAgMCmBBRI\nmxLyPAECBAgQIECAAAECzQgokJqZagMlQGDKBZ6Z/lc0AgQIECBAYIgCVrEbIq63JkCAwAoK\n/GHvvc5awff0VgQIECBAgMA8AWeQ5oF4SIAAAQIECBAgQIBAuwIKpHbn3sgJECBAgAABAgQI\nEJgnoECaB+IhAQIECBAgQIAAAQLtCiiQ2p17IydAgAABAgQIECBAYJ6AAmkeiIcECBAgQIAA\nAQIECLQrYBW7dufeyAkQmC6B9dPVXb0lQIAAAQLTKaBAms5502sCBNoTOL69IRsxAQIECBAY\nvYACafTmjkiAAIHNEbhic17kNQQIECBAgMDSBHwHaWle9iZAgAABAgQIECBAoMMCCqQOT66h\nESBAgAABAgQIECCwNAEF0tK87E2AAAECBAgQIECAQIcFFEgdnlxDI0CgUwK7ZzQVjQABAgQI\nEBiigEUahojrrQkQILCCAm/rvddLV/A9vRUBAgQIECAwT0CBNA/EQwIECEyogP9eT+jE6BYB\nAgQIdEvAJXbdmk+jIUCAAAECBAgQIEBgGQIKpGXgeSkBAgQIECBAgAABAt0SUCB1az6NhgAB\nAgQIECBAgACBZQgokJaB56UECBAgQIAAAQIECHRLQIHUrfk0GgIECBAgQIAAAQIEliFgVaRl\n4HkpAQIERihw+giP5VAECBAgQKBZAQVSs1Nv4AQITJnAWVPWX90lQIAAAQJTKeASu6mcNp0m\nQIAAAQIECBAgQGAYAgqkYah6TwIECBAgQIAAAQIEplJAgTSV06bTBAgQIECAAAECBAgMQ0CB\nNAxV70mAAAECBAgQIECAwFQKKJCmctp0mgCBBgXeljGvanDchkyAAAECBEYqYBW7kXI7GAEC\nBDZbYM/NfqUXEiBAgAABAgMLOIM0MJUdCRAgQIAAAQIECBDouoACqeszbHwECBAgQIAAAQIE\nCAwsoEAamMqOBAgQIECAAAECBAh0XUCB1PUZNj4CBAgQIECAAAECBAYWUCANTGVHAgQIECBA\ngAABAgS6LmAVu67PsPERINAVgTUZyF1dGYxxECBAgACBSRVQIE3qzOgXAQIE5gocP/ehRwQI\nECBAgMAwBFxiNwxV70mAAAECBAgQIECAwFQKtHgGacfM1A7JNslNyXXJzYlGgAABAgQIECBA\ngEDjAq2cQdo38/zJ5KpkXbI6uThZm1SR9OPkpGTnRCNAgAABAgQIECBAoFGBFs4g1XX7q3rz\nW19yvjCpIqkKozqTtFOyZ3Jc8tzkVclpiUaAAAECBAgQIECAAIFOCRyR0dSqT19KHrvIyLbI\ncwcn30xq/wOTUbZjc7A67najPKhjESAwVQLPTG8rGgECBAgQmDSBrdOh+lv2CZPWMf3ZUODU\nbKrL5+r7RoO0+n7SDcnHBtl5BfdRIK0gprci0FGBkzOuikaAAAECBCZNoFMFUte/g7RPPj11\nSd1tA36Krs1+FyV7DLi/3QgQIECAAAECBAgQ6JBA1wukn2au9ku2GnDO6gxSFVW1gINGgAAB\nAgQIECBAgEBjAl0vkE7JfO6dnJEcsMjc1neQDkrOSe6XfCHRCBAgQIAAAQIECBBoTKDrq9jV\nanS7JCcmhyWXJ7W09zVJfddo+2SnZK9kt2R98rrkgkQjQIAAAQIECBAgQIBAJwUenlF9JqkC\nqVbYmJ36kdh/T96bPDQZRzs2B60+WcVuHPqOSWA6BE5ONysaAQIECBCYNIFOLdLQ9TNI/Q/P\nJblzVO9BnTWq3z/aNqkfjr0+0QgQIDDpAnWGWyNAgAABAgSGLNBKgTSbsS6tq2gECBCYJoH6\n0WuNAAECBAgQGLJAawVSXcJW3zWq1epqgYo6e/TzpL6TpBEgQGCSBa6Y5M7pGwECBAgQIDBd\nArVCXS28cHsy+/tH/fv1Y7L1HaT7JuNovoM0DnXHJECAAAECBAgQWAmBTn0HqevLfNeEV/Fx\nXvKo5F+SK5Nq9eOxf5HUEuDVavW6byePqQcaAQIECBAgQIAAAQIEuiZwYAZUZ4k+lPTPDlVR\n+AfJhcnnki2T+h2k/5jUYg63JA9JRtmcQRqltmMRIECAAAECBAispECnziCtJMwkvte70qnv\nJ1UAzW+/mQ1VPD151hO/kft3JCfO2jaKuwqkUSg7BoHpFtg93a9oBAgQIEBg0gQ6VSB1/RK7\nQ/PpqQKpCqH5rb53VL+BNLtAujSPv5v8dqIRIEBgkgTels5UNAIECBAgQGCIAl1fxe7q2O2f\n1Djn/4bIw7Nt/g+z1uV2D03+LVlO2yovPjKpanqQ9vuD7GQfAo0L7J3xt/x/KzX+ai+556bJ\n//2njPp/NjlygyYwXoFx//f3wRl+/WN3/3vk49Dw359xqI/pmF0vkM6Na61Od1LyqqTOGFV7\nYPJXd9+bmTm/d1s/HvsnyS7J13vbNvdmt7zwzUkVSoO0Xx9kJ/sQaFzgDdtss80Ld9hhh1qN\nsrl288033/3f6+222+6xzQ0+A77++uu3uu222/4md1/c4viNmcCYBZ6W479yjH3YuXfs+mmW\ncbVa2Ms/0IxLf8THXei7OSPuwlAPV39QXJDUWaQ6m/StpNrjkwck/0/yvKTaZUktzlCX2NXz\nv0xG1Y7NgT6e3D/pF3GjOrbjEJgWgZOf/vSn/+cTTjhhWvqrnysosGrVqpmzzz77lLzlMSv4\ntt6KAIHpEDi5181jpqO7Tfayrpq6LTkwqYXQprr92lT3ftOdr8vqDknek2yZPLWX+hfoOlt0\ndNJv38idtydPTEZZHPWP75YAAQIECBAgQIAAgTELdP0Su+L9RfKGXuoa1lqlbqFTtM/Ndo0A\nAQIECBAgQIAAgYYFWiiQZk/vz2Y/cJ8AAQIECBAgQIAAAQKzBbp+id3ssQ5y/xXZqZYFf/kg\nO9uHAAECBAgQIECAAIFuCbR2BmlTs7drdtgnqVuNAAECBAgQIEBg/AIL/Z7l+HulB50VUCDN\nndqP5uHnknGusz+3Rx4RIECAAAECBNoW6P80S9sKRj8yAQXSXOoqjBRHc008IkCAAAECBAiM\nU+Br4zy4Y7cn0GKBtGOmuX4UdpvkpuS6xG8PBUEjQIAAAQIECBAg0LpAK4s07JuJ/mRyVbIu\nWZ1cnKxNqkj6cXJS0v+l5tzVCBAgQIAAAQIECBBoTaCFM0jHZ1JX9SZ2TW7r132rSKrCqM4k\n7ZTsmRyX1G8hvSo5LdEIECBAgAABAgQIEGhMoOsF0hGZzyqOzkneknwnWahtkY0HJe9LTk0u\nTb6eaAQIECBAgAABAuMVqL/TqlnN7h4H/ztkga5fYnd4/C5J6nZjxVER1//BnZ88JbkxeVGi\nESBAgAABAgQIjF/g/elCRSMwEoGun0HaJ4p1Sd1tA2pem/0uSvYYcH+7ESBAgAABAgQIDFeg\nFtjSCIxMoOtnkH4ayf2SrQYUrf8DrKKqFnDQCBAgQIAAAQIECBBoTKDrBdIpmc+9kzOSAxaZ\n2/53kOq7SvdLvrDIvp4iQIAAAQIECBAgQKCjAl2/xK5Wo9slOTE5LLk8WZtck9yQbJ/UKnZ7\nJbsl65PXJRckGgECBAgQIECAAAECjQl0vUCqxRc+kJyZvCM5OJl/JukX2XZFUivYfTC5LNEI\nECBAgAABAgQIEGhQoOsFUn9KayW7o3oP6qxR/f7Rtkn9cOz1iUaAAAECBAgQIECAAIGZVgqk\n2VNdl9ZVNAIECBAgQIAAgckXuGjyu6iHXRJosUDq0vwZCwECBAgQIECg6wLv7/oAjW+yBLq+\nit1kaesNAQIECBAgQIAAAQITLaBAmujp0TkCBAgQIECAAAECBEYpoEAapbZjESBAgAABAgQI\nECAw0QIKpImeHp0jQIAAAQIECBAgQGCUAgqkUWo7FgECBAgQIECAwFIFjs4LKhqBkQgokEbC\n7CAECBAgQIAAAQKbKXBoXlfRCIxEQIE0EmYHIUCAAAECBAgQIEBgGgQUSNMwS/pIgAABAgQI\nECBAgMBIBBRII2F2EAIECBAgQIAAAQIEpkFAgTQNs6SPBAgQIECAAAECBAiMRECBNBJmByFA\ngAABAgQIECBAYBoE7jMNndRHAgQIECBAgACBZgVua3bkBj4WAQXSWNgdlAABAgQIECBAYECB\n1w+4n90IrIiAAmlFGL0JAQIECBAgQIDAkARuGNL7elsCCwr4DtKCLDYSIECAAAECBAgQINCi\ngAKpxVk3ZgIECBAgQIAAAQIEFhRQIC3IYiMBAgQIECBAgAABAi0KKJBanHVjJkCAAAECBAhM\nj8De6epvTU939XTaBSzSMO0zqP8ECBAgQIAAgW4LvKE3vBd3e5hGNykCCqRJmQn9IECAAAEC\nBAgQWEjAFU8Lqdg2NAEfuKHRemMCBAgQIECAAAECBKZNQIE0bTOmvwQIECBAgAABAgQIDE1A\ngTQ0Wm9MgAABAgQIECBAgMC0CSiQpm3G9JcAAQIECBAgQIAAgaEJWKRhaLTemAABAgQIECBA\nYAUE7lqB9/AWBAYWUCANTGVHAgQIECBAgACBMQj81RiO6ZANCyiQGp58QydAgAABAgQITIHA\n16agj7rYIQHfQerQZBoKAQIECBAgQIAAAQLLE1AgLc/PqwkQIECAAAECBAgQ6JCAAqlDk2ko\nBAgQIECAAAECBAgsT0CBtDw/ryZAgAABAgQIEBiuwBZ5+4pGYCQCFmkYCbODECBAgAABAgQI\nbKbA+3uve81mvt7LCCxJQIG0JC47EyBAgAABAgQIjFhgxxEfz+EaF3CJXeMfAMMnQIAAAQIE\nCBAgQOBeAQXSvRbuESBAgAABAgQIECDQuIACqfEPgOETIECAAAECBAgQIHCvgALpXgv3CBAg\nQIAAAQIECBBoXECB1PgHwPAJECBAgAABAgQIELhXwCp291q4R4AAAQIECBAgMHkCF01el/So\nywIKpC7PrrERIECAAAECBKZfoP87SNM/EiOYCgGX2E3FNOkkAQIECBAgQIAAAQKjEFAgzcxs\nHejHJNuNAtwxCBAgQIAAAQIECBCYXIFWCqTnZwo+krwxeURvOu6f288mVyffS25IPp3skGgE\nCBAgQIAAAQIECDQo0PXvIFUB+PnkWbPm9k25X2eM3po8L/lK8qNk3+SFycOSg5O7Eo0AAQIE\nCBAgQIAAgYYEun4G6djMZRVHX+7dvjK31ybnJS9JjkielLws2T+poumJyZGJRoAAAQIECBAg\nMH6Bo9OFikZgJAJdP4P07CiuSw5Lbu2Jrs3tmcnZyem9bf2bd+bOcUkVSZ/pb3RLgAABAgQI\nECAwNoFDe0c+dWw9cOCmBLp+BmmvzGZdQtcvjmpy6+zRnckP6sG8VttXJ3vO2+4hAQIECBAg\nQIAAAQINCHS9QFqTOaxL6LadNZdPy/0a96NnbevfrTNqj00u7W9wS4AAAQIECBAgQIBAOwJd\nL5DqUrodk7qc7jnJnyR/ntSqdVUovSDpt7L4RFKr23010QgQIECAAAECBAgQaEyg699B+njm\n86lJfRfpkN7c/ry37e25rWtZX53U95Ien+yenJuckWgECBAgQIAAAQIECDQm0PUCqb5TdHhS\nZ48OTC5JvphcmbwhqR+JfUayf3JL8uGkfitJI0CAAAECBAgQIECgQYGuF0j9Kf187lRmt+vy\n4JikLq2rxRzWJHckGgECBAgQIECAwOQI3DY5XdGTFgRaKZAWm8sy2D6phRxuXmxHzxEgQIAA\nAQIECIxc4PUjP6IDNi3Q9UUa+pP7/Nz5SFKXzz2it7EWY/hscnVSizbckHw62SHRCBAgQIAA\nAQIEJkOg/karaARGItD1M0hVANaldc+apfmm3H9M8tbkeclXkh8l+yYvTB6WHJzclWgECBAg\nQIAAAQIECDQk0PUzSMdmLqs4+nLv9pW5vTapH4t9SXJEUr+T9LKkFmqooumJyZGJRoAAAQIE\nCBAgQIBAYwJdP4P07MznuuSw5Nbe3K7N7ZnJ2cnpvW39m3fmznFJFUmf6W90S4AAAQIECBAg\nQIBAGwJdP4NUq9PVJXT94qhmtc4e3Zn8oB7Ma7V9dbLnvO0eEiBAgAABAgQIjEdg7xz2t8Zz\naEdtUaDrBdKaTGpdQlcr1PXb03Knxv3o/oZZt3VG7bHJpbO2uUuAAAECBAgQIDA+gTfk0H6n\ncnz+zR2565fY1aV0T03qcrr6Edj6F4j6HlKtWleF0guS05JqVTR9IqnV7b6aLKfdLy+u42w9\n4Js8bsD9Wt9t/wAcOkaEPXrHvnyMfTg3x/7GGI/v0AQIECBAYNQCXf8H/VF7Ot4mBLpeIH08\n468Cqb6LdEjP4ue9bW/P7anJq5P6XtLjk92T+gP0jGQ5bYe8uAqwQQukXZdzsIZe+zs913EN\n+RG9A9eqh+NqP82BFUjj0ndcAgQIECBAoPMCXS+Q6jtFhyfPSQ5MLkm+mFyZ1OnaKmCekdSZ\niVuSOsu0Eqdw64/Y/5QM2mq1vSrmtMUFPpWnK+NqJ/cOfMy4OuC4BAgQIECAAAECwxXoeoHU\n1/t87lRmt+vy4JikTtvWYg5rkjsSjQABAgQIECBAgACBRgVaKZAWm97+ynWL7eM5AgQIECBA\ngAABAgQaEFAgNTDJhkiAAAECBAgQmGKBu6a477o+hQJWBZk7aa/Iw+8nL5+72SMCBAgQIECA\nAIExCfxVjlvRCIxEwBmkucy1mtw+iVXl5rp4dI+Af8HySSBAgAABAqMX+NroD+mILQsokObO\n/kfz8HNJrXKnEZgv8OfzN3hMgAABAgQIECDQLQEF0tz5rMJIcTTXxKN7BeryS40AAQIECBAg\nQKDDAi0WSDtmPuuHXLdJbkpque+bE40AAQIECBAgQIAAgcYFWlmkYd/M8yeTq5J1yerk4mRt\nUkXSj5OTkp0TjQABAgQIECBAYHIEtkhXKhqBkQi0cAbp+Eiu6mnWj8FemFSRVIVRnUnaKdkz\nOS55bvKq5LREI0CAAAECBAgQGL/A+3tdeM34u6IHLQh0vUA6IpNYxdE5yVuS7yQLtfpXiYOS\n9yWnJpcmX080ArMF7tt7cMvsje4TIECAAAECQxWor0doBEYm0PVL7A6P5CVJ3W6sOCrsWr75\n/OQpyY3JixKNwHyBKqArGgECBAgQIECAQEcFun4GaZ/MW11Sd9uA83dt9rso2WPA/e3WlsD9\n2hqu0RIgQIAAAQIE2hPo+hmkn2ZK90u2GnBq6xRuFVW1gINGgAABAgQIECBAgEBjAl0vkE7J\nfO6dnJEcsMjc9r+DVN9VqrMEX1hkX08RIECAAAECBAgQINBRga5fYler0e2SnJgcllyerE2u\nSW5Itk9qFbu9kt2S9cnrkgsSjQABAgQIECBAgACBxgS6XiDV4gsfSM5M3pEcnMw/k/SLbLsi\nqS/ffzC5LNEIECBAgAABAgQmQ6C+H64RGJlA1wukPmStZHdU70GdNarfP9o2qR+OvT7RCBAg\nQIAAAQIEJlPg/ZPZLb3qqkArBdLs+atL6yoagaUKfG2pL7A/AQIECBAgQIDAdAm0WCBN1wzp\n7SQJfGqSOqMvBAgQIECAAAECKy/Q9VXsVl7MOxIgQIAAAQIECBAg0FkBBVJnp9bACBAgQIAA\nAQIECBBYqoACaali9idAgAABAgQIEBilwNE5WEUjMBIBBdJImB2EAAECBAgQIEBgMwUOzesq\nGoGRCCiQRsLsIB0ReGXGUdEIECBAgAABAgQ6KmAVu45OrGENReD3hvKu3pQAAQIECBAgQGBi\nBJxBmpip0BECBAgQIECAAAECBMYtoEAa9ww4PgECBAgQIECAAAECEyOgQJqYqdARAgQIECBA\ngAABAgTGLeA7SOOeAccnQIAAAQIECBBYTOC2xZ70HIGVFlAgrbSo9yNAgAABAgQIEFhJgdev\n5Jt5LwKbElAgbUrI8wTuFbjx3rvuESBAgAABAiMSuGFEx3EYAncLKJB8EAgMLvDawXe1JwEC\nBAgQIECAwDQKKJCmcdb0eVwCt4/rwI5LgAABAgQIECAwGgGr2I3G2VEIECBAgAABAgQIEJgC\nAQXSFEySLhIgQIAAAQIEGhbYO2P/rYbHb+gjFnCJ3YjBHY4AAQIECBAgQGBJAm/o7f3iJb3K\nzgQ2U0CBtJlwXtakwP69UX+jydEbNAECBAgQGI+AK57G497sURVIzU69gW+GwCt6r1EgbQae\nlxAgQIDAZgsclFc+fbNfPf0vfGxvCO+a/qFs9gjOziu/ttmv9sIlCSiQlsRl58YFtmh8/IZP\ngAABAuMRePFOO+30woc97GHrx3P48R513bp1d59BisEjx9uT8Rx99erV94nBg3N0BdKIpkCB\nNCJohyFAgAABAgQIbKbAFo9//OO3POGEE7bczNd72RQLrFq1aubss8/2j7QjnEPXdI4Q26EI\nECBAgAABAgQIEJhsAQXSZM+P3hEgQIAAAQIECBAgMEIBBdIIsR2KAAECBAgQIECAAIHJFvAd\npMmeH72bLIG7Jqs7ekOAAAECBAgQILDSAgqklRb1fl0W+PMuD87YCBAgQIAAAQIEZmYUSD4F\nBAYX+P7gu9qTAAECBAgQIEBgGgV8B2kaZ02fCRAgQIAAAQIECBAYioACaSis3pQAAQIECBAg\nQIAAgWkUUCBN46zpMwECBAgQIECAAAECQxFQIA2F1Zt2VOC+GVdFI0CAAAECBAgQ6KiARRo6\nOrGGNRSB9/Xe9Y+G8u7elAABAgQIECBAYOwCCqSxT4EOTJHA/aaor7pKgAABAgQIECCwGQIu\nsdsMNC8hQIAAAQIECBAgQKCbAgqkbs6rUREgQIAAAQIECBAgsBkCCqTNQPMSAgQIECBAgAAB\nAgS6KaBA6ua8GhUBAgQIECBAgAABApshoEDaDDQvIUCAAAECBAgQIECgmwJWsevmvBrVcAS+\nNpy39a4ECBAgQIAAAQKTIqBAmpSZ0I9pEPjUNHRSHwkQIECAAAECBDZfwCV2m2/nlQQIECBA\ngAABAgQIdEyg9QJpy8znI5IHdGxeDYcAAQIECBAgQIAAgc0QaKFA2iUuH0v+epbPDrn/0eTm\n5N+Ta5KLktclGgECBAgQIECAAAECjQp0/TtID8q8fifZIzm/N8db5fYryWOTO5OvJlcn+yfv\nTeqM0iuTek4jQIAAAQIECBAgQKAhga6fQXpz5rKKoz9JntKb1/8jt1UcfSKp5w5Jjkj+Q/Kh\n5OXJkxKNwHyBKpwrGgECBAgQIECAQEcFul4gPSHztjr5s+S23hwelNvrkvpD92e9bXXzy+Q1\nyWXJkxONwHyB38uGikaAAAECBAgQINBRga4XSHUJ4XeT2ZfL3ZHHa5Lbk/mt9rsiqbNJGgEC\nBAgQIECAAAECjQl0vUD6dubz0OSBs+b1/Nx/ZLLzrG39uw/Onccl3+9vcEuAAAECBAgQIECA\nQDsCXS+QPpmp3Cb5XlKX1lWrH/uswunvkt2Tfvvd3KniaX3yuf5GtwQIECBAgAABAgQItCPQ\n9VXsvpWprEUX/jL5/5J/Tao4+mHykuTS5EdJnWGq5cDvSl6W1H4aAQIECBAgQIAAAQKNCXT9\nDFJNZ/3+0W8k7052TF6UvDTZIqklvx+VbJf8bbJPUqvbaQQIECBAgAABAgQINCjQ9TNI/Sm9\nMndqqe/Klkl916iW+P5FsjapVe00ApsSuHFTO3ieAAECBAgQIEBgugVaKZBmz1KtYnd5L7V9\n6+QxSV1qd3OiEdiYwGs39oTtBAgQIECAAAEC3RBo4RK7mqnnJx9J3pg8Iql2/+SzydVJLeJw\nQ/LpZIdEI7CQQC0Nv9Dy8AvtaxsBAgQIECBAgMAUCnT9DFIVgJ9PnjVrbt6U+3XG6K3J85Kv\nJHX2aN/khcnDkoOTWrBBI0CAAAECBAgQIECgIYGun0E6NnNZxdGXe7evzO21yXlJrWJ3RPKk\npFau2z+poumJyZGJRoAAAQIECBAgQIBAYwJdP4P07MznuuSw5Nbe3K7N7ZnJ2cnpvW39m3fm\nznFJFUmf6W90S4AAAQIECBAgQIBAGwJdP4O0V6axLqHrF0c1q3X26M7kB/VgXqvtq5M95233\nkEAJ1FnGikaAAAECBAgQINBRga6fQVqTeatL6LZN+kXS03K/CsNHJ/NbeTw2OXn+Ex4TiMAr\negrfoDEegfPPP3/mqKOOGs/BHXWsAlddddVYj+/gBAgQINCOQNcLpLqU7qlJXU734WTvpL6H\nVKvWVaH0guS0pFoVTfUjsbW63VeT5bQd8uITkvoh2kHaQsXaIK8b9T6H5oCzF7wY9fHHfbwD\neh2oz1Krrf5vqr7TN5Z20003zVQ0AgQIECBAgMCwBLpeIH08cFUg1XeRDukh/ry37e25PTV5\ndbI2eXyye3JuckaynLZ1XvzgpG4HaVVQTUM7etddd33h3nvvXZciNtfyL9hb1KB32WWX/9Dc\n4DPgiy+++NeuvPLK+geEsRVILbobMwECBAgQIDBaga4XSPWH/OHJc5IDk0uSLyZXJm9IqoB5\nRlLfK7klqTMD9VtJy21VhNXZqUHbsdmxirmJb/vtt9+vnXDCCV3/7trEz8M4Orhq1aqZs88+\n++4icRzHr2NutdVWM/e9733HdXjHHaPALbfcMnP77X6GbIxT4NAECBBoRqDrBVJ/Ij+fO5XZ\n7bo8OCapP/ZrMYc1yR2JRoDAhAoceuihMynQJ7R3ujVMgV6BPsxDeG8CBAgQIHC3QCsF0mLT\nXWeZauU6jQABAgQIECBAgACBxgVcKtX4B8DwCRAgQIAAAQIECBC4V0CBdK9F3atlnL+fvLwe\naAQIECBAgAABAgQItCWgQJo737vm4T5J3WoECBAgQIAAAQIECDQm4DtIcyf8o3n4uaRWudMI\nECBAgAABAgQIEGhMQIE0d8KrMFIczTXxiAABAgQIECBAgEAzAi0WSDtmduuHWbdJbkpque+b\nE40AAQIECBAgQIAAgcYFWvkO0r6Z508mVyXrklrW++JkbVJF0o+Tk5KdE40AAQIECBAgQIAA\ngUYFWjiDdHzmdlVvftfk9sKkiqQqjOpM0k7JnslxyXOTVyWnJRoBAgQIECBAgAABAo0JdL1A\nOiLzWcXROclbku8kC7UtsvGg5H3JqcmlydcTjQABAgQIECBAgACBhgS6fond4ZnLS5K63Vhx\nVNN9V3J+8pTkxuRFiUaAAAECBAgQIECAQGMCXS+Q9sl81iV1tw04r9dmv4uSPQbc324ECBAg\nQIAAAQIECHRIoOsF0k8zV/slWw04Z7XCXRVVtYCDRoAAAQIECBAgQIBAYwJdL5BOyXzunZyR\nHLDI3Pa/g1TfVbpf8oVF9vUUAQIECBAgQIAAAQIdFej6Ig21Gt0uyYnJYcnlydrkmuSGZPuk\nVrHbK9ktWZ+8Lrkg0QgQIECAAAECBAgQaEyg6wVSLb7wgeTM5B3Jwcn8M0m/yLYrklrB7oPJ\nZYlGgAABAgQIECBAgECDAl0vkPpTWivZHdV7UGeN6vePtk3qh2OvTzQCBAgQIECAAAECBAjM\ntFIgzZ7qurSuohEgQIAAAQIECBAgQGCOQNcXaZgzWA8IECBAgAABAgQIECCwmIACaTEdzxEg\nQIAAAQIECBAg0JSAAqmp6TZYAgQIECBAgAABAgQWE1AgLabjOQIECBAgQIAAAQIEmhJQIDU1\n3QZLgAABAgQIECBAgMBiAgqkxXQ8R4AAAQIECBAgQIBAUwIKpKam22AJECBAgAABAgQIEFhM\nQIG0mI7nCBAgQIAAAQIECBBoSkCB1NR0GywBAgQIECBAgAABAosJKJAW0/EcAQIECBAgQIAA\nAQJNCSiQmppugyVAgAABAgQIECBAYDEBBdJiOp4jQIAAAQIECBAgQKApAQVSU9NtsAQIECBA\ngAABAgQILCagQFpMx3MECBAgQIAAAQIECDQloEBqaroNlgABAgQIECBAgACBxQSWWiAduNib\n9Z77ndw+b4D97EKAAAECBAgQIECAAIGJElhqgfR/p/cfSrZZYBRbZNtrk28mj1rgeZsIECBA\ngAABAgQIECAw0QJLLZB+mNH8l+Sfk0fOGtlDcv/c5H3JuuS8RCNAgAABAgQIECBAgMBUCdxn\nib19Vvb/r8lbk+8kr0xuST6W7JickvyfyXWJ1kGBf/zHf5z57ne/28GRGdKmBK67zv9Zb8rI\n8wQIECBAgMD0Cyy1QLojQ16V/EPy6eTkpNplydHJl+qB1l2BW265ZaaiESBAgMBIBZ6Zo/3h\nSI8492B1pUi1tffcjOV/T89RzxrLkR2UAIGmBJZaIPVxbs2d6/sPerdVPGkECBAgQIBA9wT2\n6g1pnAVS91SNiACBiRRYaoFUizOckLy+N5q6/2/JXyZ/n3wyeV1yQ6J1UOC+973vzAMe8IAO\njsyQNiVQl9g5e7gpJc8TGJpAnTkZ59mTk3sjO6Z364YAAQKdFVhqgfTlSDwx+VFSl9R9I6n2\nT0l9/+ilyf+a1DLftZCD1jGBQw45ZOaEE6ou1loTWLVq1czZZ5/d2rCNlwABAgQIEGhMYKmr\n2O0Rn08kv5v0i6MiW5s8OamzR7skVSRpBAgQIECAAAECBAgQmCqB+yyxty/M/hds5DV3Zfv7\nk3MTv4O0ESSbCRAgQIAAAQIECBCYXIGlFkgbK45mj/Bf86CiESBAgAABAgQIECBAYKoEllog\nTdXgdJYAAQIECBBYEYH1K/Iu3oQAAQJTIKBAmoJJ0kUCBAgQIDBmgePHfHyHJ0CAwMgEFEgj\no3YgAgQIECAwtQJXTG3PdZwAAQJLFFjqKnZLfHu7EyBAgAABAgQIECBAYHoEFEjTM1d6SoAA\nAQIECBAgQIDAkAUUSEMG9vYECBAgQIAAAQIECEyPgAJpeuZKTwkQIECAwLgEds+BKxoBAgQ6\nL2CRhs5PsQESIECAAIFlC7yt9w4vXfY7eQMCBAhMuIACacInSPcIECBAgMAECPh7YQImQRcI\nEBiNgEvsRuPsKAQIECBAgAABAgQITIGAAmkKJkkXCRAgQIAAAQIECBAYjYACaTTOjkKAAAEC\nBAgQIECAwBQIKJCmYJJ0kQABAgQIECBAgACB0QgokEbj7CgECBAgQIAAAQIECEyBgFVppmCS\ndJEAAQIECIxZ4PQxH9/hCRAgMDIBBdLIqB2IAAECBAhMrcBZU9tzHSdAgMASBVxiNzOzc8z2\nTlgs8cNjdwIECBAgQIAAAQJdE1AUzMz8cSb1h8kDuja5xkOAAAECBAgQIECAwNIEun6J3T7h\n2G4TJHv0nv+93N7Qu39Zbtf27rshQIAAAQIECBAgQKARga4XSJ/OPD5mwLk8Z9Z+f5r7q2Y9\ndpcAAQIECBAgQIAAgQYEul4gfSxz+IFk2+SLSV1KN78dkg37Jx9Kbuk9eUHv1g0BAgQIECAw\nM/O2INyVnACDAAECXRdooUD6WibxtOTQ5MvJR5L6j3y/vTt3qkCqM0br+hvdEiBAgAABAr8S\n2PNX99whQIBAxwVaWKThf2QOqwD6y+SDyd8n/e8d5a5GgAABAgQIECBAgACBewRaKJBqpLcl\ntVrdk5NHJf+aHJloBAgQIECAAAECBAgQ+JVAKwVSf8BfyZ1a2e7c5DNJXXq3Y6IRIECAAAEC\nBAgQIEBgpuvfQVpoiq/Nxucn9avg9X2k7RONAAECBAgQIECAAAECM62dQZo95X+TB7UE+OnJ\nV5PbE40AAQIECBAgQIAAgYYFWjyDNHu6L82Do5P6XtKdiUaAAAECBAhsKLAmm2avALvhHrYQ\nIECgIwKtFEh1Sd1ByWXJGcmPkvsnn0qelvx6UgXSqcl/Sa5PNAIECBAgQOAegeNBECBAoBWB\nrhdIdQnh55NnzZrQN+V+XVr31uR5SS3cUAXTvskLk4clByf+pSwIGgECBAgQIECAAIGWBLr+\nHaRjM5lVHNUPxNbtK5NapOG85CXJEcmTkpcl9VtJVTQ9MbEEeBA0AgQIECBAgAABAq0JdP0M\n0rMzoeuSw5Jbe5O7NrdnJmcntUDD7PbOPDguqSKplgHXCBAgQIAAAQIECBBoSKDrZ5D2ylzW\nJXT94qimts4e3Zn8oB7Ma7V9dbLnvO0eEiBAgAABAgQIECDQgEDXC6Q1mcO6hG7bWXNZizLU\nuB89a1v/bp1Re2xyaX+DWwIECBAgQGDmmTGoaAQIEOi8QNcvsatL6Z6a1OV0H072Tup7SN9L\nqlB6QXJaUq2Kpk8ktbrdV5PltAflxR9Kth7wTX5jwP3sRoAAAQLjEfjDLbfcsn4Wosl2xx13\n1D8ezsSgvr/bZItBrXQ7/9L8Ji0MmkDXBbpeIH08E1gFUn0X6ZDeZP68t+3tua3/2L06qe8l\nPT7ZPTk3qaXAl9Nuz4t/lmw14JvsOOB+diNAgACB8Qg88yEPecjh++9f6/m01372s5/NbLHF\nFjO77rprk5egf+Mb35j5yU9+cn1mXoHU3sffiBsU6HqBVN8pOjx5TnJgcknyxeTK5A1JneF5\nRlL/H++WpM4yvTFZbqv/iL52CW9Sq+39pyXsb1cCBAgQGLHAb//2b8/88R//8YiP6nCTILBq\n1aoqkCahK/pAgMAIBLpeIPUJP587ldntujw4JqlL62oxhzXJHYlGgAABAgQIECBAgECjAq0U\nSItNb51lqpXrNAIECBAgQIAAAQIEGheosycaAQIECBAgQIAAAQIECERAgTT3Y/CKPPx+8vK5\nmz0iQIAAAQIECBAgQKAFAQXS3FneNQ/3SepWI0CAAAECBAgQIECgMQHfQZo74R/Nw88ltcqd\nRoAAAQIECBAgQIBAYwIKpLkTXoWR4miuiUcECBAgQIAAAQIEmhFosUDaMbO7Q7JNclNSy33f\nnGgECBAgQIAAAQIECDQu0Mp3kPbNPH8yuSpZl9Sy3hcna5Mqkn6cnJTsnGgECBAgQIAAAQIE\nCDQq0MIZpOMzt6t687smtxcmVSRVYVRnknZK9kyOS56bvCo5LdEIECBAgAABAgQIEGhMoOsF\n0hGZzyqOzkneknwnWahtkY0HJe9LTk0uTb6eaAQIECBAgAABAgQINCTQ9UvsDs9cXpLU7caK\no5ruu5Lzk6ckNyYvSjQCBAgQIECAAAECBBoT6HqBtE/msy6pu23Aeb02+12U7DHg/nYjQIAA\nAQIECBAgQKBDAl0vkH6audov2WrAOasV7qqoqgUcNAIECBAgQIAAAQIEGhPoeoF0SuZz7+SM\n5IBF5rb/HaT6rtL9ki8ssq+nCBAgQIAAAQIECBDoqEDXF2mo1eh2SU5MDksuT9Ym1yQ3JNsn\ntYrdXsluyfrkdckFiUaAAAECBAgQIECAQGMCXS+QavGFDyRnJu9IDk7mn0n6RbZdkdQKdh9M\nLks0AgQIECBAgMDECKxevXrmtNPq33211gRq7rXRCnS9QOpr1kp2R/Ue1Fmj+v2jbZP64djr\nE40AAQIECBAgMLECP/zhD2cqGgECwxdopUCaLVmX1lU0AgQIECBAgAABAgQIzBHo+iINcwbr\nAQECBAgQIECAAAECBBYTaPEM0mIeniNAgAABAgQITJzA4x73uJkjjzxy4vqlQ8MX+Nu//duZ\nb33rW8M/kCP8SkCB9CsKdwgQIECAAAECkymwyy67zBx00EGT2Tm9GqrAV77ylaG+vzffUMAl\ndhua2EKAAAECBAgQIECAQKMCCqRGJ96wCRAgQIAAAQIECBDYUECBtKGJLQQIECBAgAABAgQI\nNCqgQGp04g2bAAECBAgQIECAAIENBRRIG5rYQoAAAQIECBAgQIBAowIKpEYn3rAJECBAgAAB\nAgQIENhQQIG0oYktBAgQIECAAAECBAg0KqBAanTiDZsAAQIECBAgQIAAgQ0FFEgbmthCgAAB\nAgQIECBAgECjAgqkRifesAkQIECAAAECBAgQ2FBAgbShiS0ECBAgQIAAAQIECDQqoEBqdOIN\nmwABAgQIECBAgACBDQUUSBua2EKAAAECBAgQIECAQKMCCqRGJ96wCRAgQIAAAQIECBDYUECB\ntKGJLQQIECBAgAABAgQINCqgQGp04g2bAAECBAgQIECAAIENBe6z4SZbCGxc4J//+Z/v+KM/\n+qP1G9+ju8+sW7fu7n9Q2Gmnne7s7ig3PrLVq1fXfy/u2vgew3/G529mxudv+J8zRyBAgACB\ntgUUSG3P/1JH/6kUCT9Nlvq6ruz/jBpICoX/1pUBbcY4zt6M16zUS3z+Iunzt1IfJ+9DgAAB\nAgQWFlAgLexi68ICX8vmSqttt97A/6RVgDGP2+fvngnw+RvzB9HhCRAgQKDbAgqkbs+v0REg\n0B2BJi/t7M70GQkBAgQITIuAAmlaZko/J0HgjknohD40K/BnGflYvwPWrLyBEyBAgEBTAgqk\npqbbYJcpcOIyX+/lBJYjcPFyXuy1BAgQIECAwGACCqTBnOxFoARWYyBAgAABAgQIEOi2gN9B\n6vb8Gh0BAgQIECBAgAABAksQUCAtAcuuBAgQIECAAAECBAh0W0CB1O35NToCBLojsH2GUtEI\nECBAgACBIQr4DtIQcb115wQe1BvR1Z0bmQFNg8B7ep182TR0Vh8JECBAgMC0CiiQpnXm9Hsc\nAu/qHfTYcRzcMZsX2KZ5AQAECBAgQGAEAgqkESA7RGcEturMSAyEAAECBAgQIEBgQQHfQVqQ\nxUYCBAgQIECAAAECBFoUUCC1OOvGTIAAAQIECBAgQIDAggIKpAVZbCRAgAABAgQIECBAoEUB\nBVKLs27MBAgQIECAAAECBAgsKGCRhgVZbCRAgMDECZw7cT3SIQIECBAg0EEBBVIHJ9WQhiZw\n1tDe2RsT2LTAqZvexR4ECBAgQIDAcgUUSMsV9PqWBE5vabDGSoAAAQIECBBoUcB3kFqcdWMm\nQIAAAQIECBAgQGBBAQXSgiw2EiBAgAABAgQIECDQooACqcVZN2YCBAgQIECAAAECBBYUaK1A\n2tR4t4zSjsm2C2rZSIAAgfEJvDaHrmgECBAgQIDAEAU2VTAM8dAje+tdc6TPJuuSG5J/TH4/\nWaj9TjbWfm9c6Enbmhd4cwQqGoFxCOyTg1Y0AgQIECBAYIgCXS+Q7h+7bybPS+rs0NrkD5Lz\nk3ckGoGlCDwyO1c0AgQIECBAgACBjgp0vUB6febtocmq5CHJ3snvJf89qTMB70+YHkarAAAs\nG0lEQVQ0AgQIECBAgAABAgQI3C3Q9QLpwIzyquTE5Ma7Rzwz8+3cHpx8LXlNUkWURoAAAQIE\nCBAgQIAAgZmuF0h7ZI6rEFo/b66vz+NnJhcl707qEjyNAAECBAgQIECAAIHGBbpeIP0k8/vk\nZKFV6WrBhqcn9b2kU5KNLdyQpzQCBAgQIECAAAECBFoQ6HqBdF4mcYfkncnuC0zo5dl2aFKX\n352dPCPRCBAgMIkC16ZTFY0AAQIECBAYokDXC6SPxO4HSX3X6LLkyGR++5/Z8JTkzqS+q1Rt\ni3tu/C+BOQJX5lFFIzAOgfoNpIpGgAABAgQIDFGg6wXSrbE7IPlQsib5ZbJQ+142Pi45Z6En\nbSPQE6jfx/IbWT4O4xK4KweuaAQIECBAgMAQBe4zxPeelLe+KR15dS+LFYQ/zj5PS2oZ8Cqs\nNAIECBAgQIAAAQIEGhNooUCaPaV1Gd38tnU2PCr5UXJzUj8sqxEgQIAAAQIECBAg0KDAYmdU\nusTx/Aymvo9Ul0c9ojew++f2s8nVSV1iV6vafTqpRR00AgQIECBAgAABAgQaFOj6GaQqAD+f\nPGvW3L4p9x+TvDWp3z/6SlJnj/ZNXpg8LKkfknWtfxA0AgQmRuCgXk/qt900AgQIECBAYEgC\nXS+Qjo1bFUdfTmqhhocmf5ycl/xmckRyetJv/zV33p4cmXymv9EtgZ5ALQlfhXN9njQCoxZ4\nce+ACqRRyzseAQIECDQl0PUC6dmZzXXJYUl/4YW1uX9mUr97NLs4ysO7fy/puNw+MVEglYg2\nW+DoPFAgzRZxf5QCfn5glNqORYAAAQLNCnS9QNorM1uX0PWLo5roOntUizXU7yPNb7V9dbLn\n/Cc8JtAT8EeqjwKBRgXuuuuumfXr1zc6+raHXXOvESDQjkDXC6Q1mconJdsm/SKplvKu7yY9\nOpnfyuOxycnzn/CYAAECBNoW+NKXvjRT0QgQIECg2wJdL5DqUrqnJnU53YeTvZNXJrVqXRVK\nL0hOS6pV0fSJpFa3+2qynLZbXlzvu9WAb7LrgPvZjQABAgQIECBAgACBIQp0vUD6eOyqQKrv\nIh3Sc/x5b1stxnBq8upkbfL4ZPfk3OSMZDnt+ry4irKtB3yTx2W/Rwy4r90IECBAgAABAgQI\nEBiSQNcLpPpO0eHJc5IDk0uSLyZXJm9IqoB5RrJ/cktSZ5nqt5KW236RN3jPEt7k2Oxb/dQI\nECCwMYH675k2RoEHPvCBMw9/+MPH2AOHHpfAJZdcMnPNNdeM6/COS4DAiAW6XiD1OT+fO5XZ\n7bo8OCapS+tqMYc1yR2JRmBjAj4fG5OxfRQCf5aD+Kb4KKQ3cowDDjhg5oQTTtjIszZ3WWDV\nqlUzZ59dF4ZoBAi0INBKgbTYXNa/yq5ebAfPEegJnEiCwBgFLh7jsR2aAAECBAg0I6BAamaq\nDXQFBBTSK4DoLQgQIECAAAECkyxQl5dp9wq8Ine/n7z83k3uESBAgAABAgQIECDQioACae5M\n13Lb+ySW3Z7r4hEBAgQIECBAgACBJgRcYjd3mj+ah59LapU7jQABApMksH2vMzdMUqf0hQAB\nAgQIdE1AgTR3RqswUhzNNfHoXoEH9e5efe8m9wiMTKD/0wEvG9kRHYgAAQIECDQo0GKBtGPm\neYdkm+SmpJb7vjnRCGxK4F29Hep3qzQCoxao/2ZpBAgQIECAwJAFWvkO0r5x/GRyVbIuqdXI\nasnctUkVST9OTkp2TjQCGxPYKk9UNAIECBAgQIAAgY4KtHAG6fjM3are/NWPwV6YVJFUhVGd\nSdop2TM5Lnlu8qrktEQjQIAAAQIECBAgQKAxga4XSEdkPqs4Oid5S/KdZKG2RTYelLwvOTW5\nNPl6ohEgQIAAAQIECBAg0JBA1y+xOzxzeUlStxsrjmq670rOT56S3Ji8KNEIECBAgAABAgQI\nEGhMoOsF0j6Zz7qk7rYB5/Xa7HdRsseA+9uNAAECBAgQIECAAIEOCXT9ErufZq72S+qL9bcP\nMG+1wl0VVbVgg0aAAIFJEjh3kjqjLwQIECBAoKsCXT+DdEombu/kjOSARSax/x2k+q7S/ZIv\nLLKvp9oVOCtDr2gExiFQ34+saAQIECBAgMAQBbp+BqlWo9slOTE5LLk8WZtck9Sv0W+f1Cp2\neyW7JeuT1yUXJBqB+QKnz9/gMQECBAgQIECAQLcEul4g1eILH0jOTN6RHJzMP5P0i2y7IqkV\n7D6YXJZoBAgQIECAAAECBAg0KND1Aqk/pbWS3VG9B3XWqH7/aNukfjj2+kQjQIAAAQIECBAg\nQIDATCsF0uyprkvrKhoBAgQIECBAgAABAgTmCHR9kYY5g/WAAAECUyzw2vS9ohEgQIAAAQJD\nFGjxDNIQOb11xwXe3BvfOzs+TsObTIH6CQKNAAECBAgQGLKAAmnIwN6+UwKP7NRoDIYAAQIE\nCBAgQGADAZfYbUBiAwECBAgQIECAAAECrQookFqdeeMmQIAAAQIECBAgQGADAQXSBiQ2ECBA\ngAABAgQIECDQqoACqdWZN24CBAgQIECAAAECBDYQsEjDBiQ2ECBAYCIFrp3IXukUAQIECBDo\nmIACqWMTajhDFbhyqO/uzQksLuA3kBb38SwBAgQIEFgRAQXSijB6k0YE3tjIOA1zMgXumsxu\n6RUBAgQIEOiWgO8gdWs+jYYAAQIECBAgQIAAgWUIKJCWgeelBAgQIECAAAECBAh0S0CB1K35\nNBoCBAgQIECAAAECBJYhoEBaBp6XEiBAYIQCB+VYFY0AAQIECBAYooBFGoaI6607J3BoRlRf\nlP9y50ZmQNMg8OJeJ782DZ3VRwIECBAgMK0CCqRpnTn9HofA0TmoAmkc8o5ZAltgIECAAAEC\nBIYv4BK74Rs7QrcE/JHarfk0GgIECBAgQIDAHAEF0hwODwgQIECAAAECBAgQaFlAgdTy7Bs7\nAQIECBAgQIAAAQJzBBRIczg8IECAAAECBAgQIECgZQGLNLQ8+8ZOgMA0Cdw5TZ3VVwIECBAg\nMK0CCqRpnTn9HofAHeM4qGMS6An8WW5rFUWNAAECBAgQGKKAAmmIuN66cwIndm5EBjRNAhdP\nU2f1lQABAgQITKuAAmlaZ06/xyGwehwHdUwCBAgQIECAAIHRCVikYXTWjkSAAAECBAgQIECA\nwIQLKJAmfIJ0jwABAgQIECBAgACB0QkokEZn7UgECBBYjsD2eXFFI0CAAAECBIYo4DtIQ8T1\n1p0TeFBvRFd3bmQGNA0C7+l18mXT0Fl9JECAAAEC0yqgQJrWmdPvcQi8q3fQY8dxcMdsXmCb\n5gUAECBAgACBEQgokEaA7BCdEdiqMyMxEAIECBAgQIAAgQUFfAdpQRYbCRAgQIAAAQIECBBo\nUUCB1OKsGzMBAgQIECBAgAABAgsKKJAWZLGRAAECBAgQIECAAIEWBRRILc66MRMgQIAAAQIE\nCBAgsKCARRoWZLGRAAECEydw7sT1SIcIECBAgEAHBRRIHZxUQxqawFlDe2dvTGDTAqduehd7\nECBAgAABAssVUCAtV9DrWxI4vaXBGisBAgQIECBAoEUB30FqcdaNmQABAgQIECBAgACBBQUU\nSAuy2EiAAAECBAgQIECAQIsCCqQWZ92YCRAgQIAAAQIECBBYUECBtCCLjQQIEJg4gdemRxWN\nAAECBAgQGKKARRqGiOutOyfw5t6I3tm5kRnQNAjsMw2d1EcCBAgQIDDtAi0WSDtm0nZItklu\nSq5Lbk40ApsSeOSmdvA8AQIECBAgQIDAdAu0condvpmmTyZXJeuS1cnFydqkiqQfJyclOyca\nAQIECBAgQIAAAQKNCrRwBun4zO2q3vyuye2FSRVJVRjVmaSdkj2T45LnJq9KTks0AgQIECBA\ngAABAgQaE+h6gXRE5rOKo3OStyTfSRZqW2TjQcn7kvq1+kuTrycaAQIECBAgQIAAAQINCXT9\nErvDM5eXJHW7seKopvuu5PzkKcmNyYsSjQABAgQIECBAgACBxgS6fgZpn8xnXVJ324Dzem32\nuyjZY8D97UaAAIFRCdR/nzQCBAgQIEBgyAJdL5B+Gr/9kq2S2wewrBXuqqiqBRs0AvMFrpy/\nwWMCIxTwG0gjxHYoAgQIEGhXoOuX2J2Sqd07OSM5YJFp7n8Hqb6rdL/kC4vs66l2Bd6YoVc0\nAuMQqEuBKxoBAgQIECAwRIGun0Gq1eh2SU5MDksuT9Ym1yQ3JNsntYrdXsluyfrkdckFiUaA\nAAECBAgQIECAQGMCXS+Q6l9bP5CcmbwjOTiZfybpF9l2RVIr2H0wuSzRCBAgQIAAAQIECBBo\nUKDrBVJ/Smslu6N6D+qsUf3+0bZJ/XDs9YlGgAABAgQIECBAgACBmVYKpNlTXZfWVfpt69x5\nVPKj5Ob+RrcECBCYMIH6rbZqX7vnxv8SIECAAAECwxDo+iINfbPn585HkvqC/SN6G++f288m\nVyffS6po+nRSZ5c0AgsJHJqNT17oCdsIjEDgxTlGRSNAgAABAgSGKND1M0hVAH4+edYswzfl\n/mOStybPS76S1NmjfZMXJg9L6rtKVosKgjZH4Og8qs/Fl+ds9YDAaARqtU2NAAECBAgQGLJA\nFRBdbsdmcFUc1R+0dfvK5NrkvOQlyRHJk5KXJfsnVTQ9MTky0QgsJOCP1IVUbCNAgAABAgQI\ndESg62eQnp15WpfUEt+39uZsbW5rVbuzk9N72/o378yd45Iqkj7T3+iWAAECBAgQIECAAIE2\nBLp+Bql+36guoesXRzWrdfbozuQH9WBeq+2rkz3nbfeQAAECBAgQIECAAIEGBLpeIK3JHNYl\ndLWkd789LXdq3I/ub5h1W2fUHptcOmubuwQIECBAgAABAgQINCLQ9Uvs6lK6pyZ1Od2Hk72T\n+h5SrVpXhdILktOSalU0fSKp1e2+miyn1Rmov0+2GvBNfn3A/exGgMD4BF6TQ9d/P8bVdu4d\nuC4BHlf7ixz4A+M6+JiPe+d55523/lvf+tbtY+7HWA5/88033/33wnbbbbd+LB0Y80Gvv/76\n+v/ndZWJRoBAAwJdL5A+njmsAqm+i3RIbz5/3tv29tyemrw6WZs8Ptk9OTc5I1lO+1leXN9n\n2nrANzko+/3nAfe12/gE7hjfoR15AgS+lD7M/g21UXfpwTlgraJ45agPPOt4/zTrfmt3/+y2\n22674Kqr6vfFm2z/e406hdJfNzn6ewbd8ue/4Wk39BYFul4g1b/2HJ48JzkwuST5YlJ/YLwh\nqQLmGcn+yS1JnWWq30pabvtl3uBvlvAmdfZKgbQEsDHteuKYjuuwkyFwcbpR0doUaH3+n9Cb\n9k+1Of1GTYBASwJdL5D6c/n53KnMbtflwTFJFSd7JWsSZwiCoG1UYPVGn/EEAQIEui1wfLeH\nZ3QECBC4V6CVAuneEW94r84y+cN3QxdbCBAgQIBAX+CK/h23BAgQ6LpAnT3RCBAgQIAAAQIE\nCBAgQCACCqS5H4NX5OH3k5fP3ewRAQIECBAgQIAAAQItCCiQ5s7yrnm4T1K3GoH5Ag/KhopG\ngAABAgQIECDQUQHfQZo7sR/Nw88l41xGd26PPJokgXf1OnPsJHVKXwgQIDACgfoZjGq+i3SP\ng/8lQKDDAgqkuZNbhZHiaK6JR/cKDPrDv/e+wj0CBAh0Q+BtvWG8tBvDMQoCBAhsXKDFAmnH\ncOyQbJPclNRy3zcnGgECBAgQILCwQIt/LywsYSsBAp0XaOU7SPtmJj+Z1E+gr0tqWe/60b+1\nSRVJP05OSnZONAIECBAgQIAAAQIEGhVo4V+E6sftVvXmd01uL0yqSKrCqM4k7ZTsmRyXPDd5\nVXJaohEgQIAAAQIECBAg0JhA1wukIzKfVRydk7wl+U6yUNsiGw9K3pecmlyafD3RCBAgQIAA\nAQIECBBoSKDrl9gdnrm8JKnbjRVHNd13JecnT0luTF6UaAQIECBAgAABAgQINCbQ9TNI+2Q+\n65K62wac12uz30XJHgPub7e2BM5qa7hGS4AAAQIECBBoT6DrBdJPM6X7JbU88+0DTG+tcFdF\nVS3YoBGYL3D6/A0eEyBAoBEB//1rZKINkwCBmZmuX2J3SiZ57+SM5IBFJrz/HaT6rtL9ki8s\nsq+nCBAgQIBAawJ1Bt1Z9NZm3XgJNCrQ9TNItRrdLsmJyWHJ5cna5JrkhmT7pFax2yvZLVmf\nvC65INEIECBAgAABAgQIEGhMoOsFUi2+8IHkzOQdycHJ/DNJv8i2K5Jawe6DyWWJRoAAAQIE\nCBAgQIBAgwJdL5D6U1or2R3Ve1Bnjer3j7ZN6odjr080AgQIECBAgAABAgQIzLRSIM2e6rq0\nrqIRWKrAm3sveOdSX2h/AgQIECBAgACB6RBosUCajpnRy0kUeOQkdkqfCBAgMAKBt+UYddn6\nCSM4lkMQIEBgrAIKpLHyOzgBAgQIEJgKgT2nopc6SYAAgRUQ6Poy3ytA5C0IECBAgAABAgQI\nEGhFQIHUykwbJwECBAgQIECAAAECmxRQIG2SyA4ECBAgQIAAAQIECLQioEBqZaaNkwABAgQI\nECBAgACBTQpYpGGTRHYg8CuBK391zx0CBAgQIECAAIFOCiiQOjmtBjUkgTcO6X29LQECBCZd\nYE06WMt8awQIEOi8gAKp81NsgAQIECBAYNkCxy/7HbwBAQIEpkTAd5CmZKJ0kwABAgQIECBA\ngACB4QsokIZv7AgECBAgQIAAAQIECEyJgAJpSiZKNwkQIECAAAECBAgQGL6AAmn4xo7QHYFD\nM5Qnd2c4RkKAAAECBAgQIDBfwCIN80U8JrBxgaPzVK3i9OWN7+IZAgQIdFLgmb1RndXJ0RkU\nAQIEZgkokGZhuEtgAIEtBtjHLgQIEOiawB/2BqRA6trMGg8BAhsIuMRuAxIbCBAgQIAAAQIE\nCBBoVUCB1OrMGzcBAgQIECBAgAABAhsIKJA2ILGBAAECBAgQIECAAIFWBRRIrc68cRMgQIAA\nAQIECBAgsIGARRo2ILFhggXelL69Zoz9+/XesZ82xj58IMf+v8Z4fIcmQIAAgdEL3PkP//AP\nd5x//vnrR3/o8R/xl7/85ZbVi6233vqO8fdm9D249dZb6+/1Jsc+eu17jqhAGpe8426OwGfz\noks254Ur9Jqde+/z8xV6v815m29uzou8hgABAssUaPIP82WareTL375+/fpzbrrpppV8z2l6\nr5dVZ1MonTRNnV7hvvr//ysM6u0mX+DYdLF+X2e7ye+qHhIgQIBAgwK7Z8wVjcA4BHz+xqG+\ntGNund3rb9knLO1lk7m3M0iTOS96RYAAAQIEJkngiknqjL40J+Dz19yUj3fAFmkYr7+jEyBA\ngAABAgQIECAwQQIKpAmaDF0hQIAAAQIECBAgQGC8Agqk8fo7OgECBAgQIECAAAECEySgQJqg\nydAVAgQIECAwoQK+JD+hE9NIt3z+GpnoSRmmRRomZSb0gwABAgQITK7A23pde+nkdlHPOizg\n89fhyZ3EoSmQJnFW9IkAAQIECEyWgL8XJms+WuuNz19rMz7m8brEbswT4PAECBAgQIAAAQIE\nCEyOgAJpcuZCTwgQIECAAAECBAgQGLOAAmnME+DwBAgQIECAAAECBAhMjoACaXLmQk8IECBA\ngAABAgQIEBizgAJpzBPg8AQIECBAgAABAgQITI6AVUEmZy70hAABAgQITKrA6ZPaMf1qQsDn\nr4lpnpxBKpAmZy70hAABAgQITKrAWZPaMf1qQsDnr4lpnpxBusRucuZCTwgQIECAAAECBAgQ\nGLOAAmnME+DwBAgQIECAAAECBAhMjoACaXLmQk8IECBAgAABAgQIEBizgAJpzBPg8AQIECBA\ngAABAgQITI6AAmly5kJPCBAgQIDApAq8LR1bNamd06/OC/j8dX6KJ2uAVrGbrPnQGwIECBAg\nMIkCe05ip/SpGQGfv2amejIG6gzSzMzWmYrHJNtNxpToBQECBAgQIECAAAEC4xJopUB6foA/\nkrwxeUQP+/65/WxydfK95Ibk08kOiUaAAAECBAgQIECAQIMCXb/ErgrAzyfPmjW3b8r9OmP0\n1uR5yVeSHyX7Ji9MHpYcnNyVaAQIECBAgAABAgQINCTQ9TNIx2Yuqzj6cu/2lbm9NjkveUly\nRPKk5GXJ/kkVTU9Mjkw0AgQIECBAgAABAgQaE+j6GaRnZz7XJYclt/bmdm1uz0zOTk7vbevf\nvDN3jkuqSPpMf6NbAgQIECBAgAABAgTaEOh6gbRXprEuoesXRzWrdfbozuQH9WBeq+2rkz3n\nbfeQAAECBAi0LLAmg3fpecufgPGO3edvvP6O3jGBL2U8dQZp21nj+sPcr//I/7dZ2/p3q2C8\nMflwf8OIbutSwOqTlfRGBO4wBAgQIECAAAECKyZQq0LX37JPWLF3HOMbdf07SHUp3Y5JXU73\nnORPkj9PatW6pyUvSPqtLD6R1Op2X000AgQIECBAgAABAgQIdEqgip4vJFXR9nNV7u+afLy3\n7V9ye0Zyee/xP+R21M0ZpFGLOx4BAgQIECBAgMBKCXTqDNJKoUz6+9TZo/ckr0j26HX2Abk9\nOfl5UsXTL5IPJfdNRt0USKMWdzwCBAgQIECAAIGVElAgrZTkhLxPnWWq3z7acoz9USCNEd+h\nCRAgQIAAAQIEliXQqQKp699Benimun4UdrHWX7nujsV28hwBAgQIEGhY4JkZe0UjMA4Bn79x\nqDd8zK4XSCdkbmtBhpOSqmw1AgQIECBAYOkCtQJsRSMwDgGfv3GoN3zMrhdI/ak9LncuTPbr\nb3BLgAABAgQIECBAgACB+QItFUj146+1Yt1fJL85H8JjAgQIECBAgAABAgQItFIg/V2m+n9J\n/t/kj5J/T+q3kZ6RtGKQoWoECBAgQIAAAQIECCwm0FJxcGUgarnvo5OLk6clZyVVLL05eXKy\nW6IRIECAAAECBAgQINCoQEsFUn+KT8udRycHJZ9Oqih6R3JuckVyTVLfWdIIECBAgAABAgQI\nEGhM4D6NjXf2cP8pDyqvSv63pJYDf1RSxdNyzyQ9PO/x7WTrZJDW/w2mWnJcI0CAAAEC8wWO\nz4Y3zt84wsf9/392xAiPOf9Q786Gt83f6PFIBHz+ZmZ8/kbyUZuMg7RcIPVn4Prc+ev+g97t\ncs+sXZr3eV6yVe/9NnVThdl7E7/FtCkpzxMgQKBNgU9m2N8a49B36h173Rj7UD/boY1HwOfv\nnp+NGY++o45cQIG0MPlyz+TU6+uSvUHbtYPuaD8CBAgQaFKgLgGvaATGIeDzNw51xxybwHLP\nlIyt4wMe+GXZb/ukzhJpBAgQIECAAAECBAgQWFSg62eQbs3oKxoBAgQIECBAgAABAgQ2KdD1\nM0ibBLADAQIECBAgQIAAAQIE+gIKpL7EPbevyM33k5fP3ewRAQIECBAgQIAAAQItCCiQ5s7y\nrnm4T1K3GgECBAgQIECAAAECjQl0/TtIS53Oj+YFn0uuXOoL7U+AAAECBAgQIECAwPQLKJDm\nzmEVRoqjuSYeESBAgAABAgQIEGhGoMUCacfM7g7JNslNyXXJzYlGgAABAgQIECBAgEDjAq18\nB2nfzHP9CvRVSf0K+Ork4mRtUkXSj5OTkp0TjQABAgQIECBAgAABAp0VOD4ju6uXn+T268lZ\nyd8mX0r+JflpUvtcnbwgGXV7Qg5Yx9961Ad2PAIECBAgQIAAAQLLFKi/Yetv2fqbVptwgSPS\nv5qsKoQeu0hft8hzByffTGr/A5NRNgXSKLUdiwABAgQIECBAYCUFFEgrqTnk9zo171+Xz9X3\njQZp9f2kG5KPDbLzCu6jQFpBTG9FgAABAgQIECAwUoFOFUhd/w5S/abRhcltA35Ers1+FyV7\nDLi/3QgQIECAAAECBAgQ6JBA1wuk+m7RfslWA85ZnUGqoqoWcNAIECBAgAABAgQIEGhMoOsF\n0imZz72TM5IDFpnb+g7SQck5yf2SLyQaAQIECBAgQIAAAQKNCXT9d5BOy3zukpyYHJZcntTS\n3tck9V2j7ZOdkr2S3ZL1yeuSCxKNAAECBAgQIECAAAECnRR4eEb1maQKpFqlbnbqR2L/PXlv\n8tBkHM0iDeNQd0wCBAgQIECAAIGVEOjUIg1dP4PUn/BLcueo3oM6a7RDsm1SPxx7faIRIECA\nAAECBAgQIEBgppUCafZU16V1FY0AAQIECBAgQIAAAQJzBFoskOYATNiDOj2pTbbAoCsiTvYo\n9I4AAQIECEyXwO3T1d3metupv2EVSJPx+e3/H/2Nk9EdvSBAgAABAgQIECCwZIFfLvkVE/iC\nWt5amwyBx6Ubzk5MxlxsrBd/mifun5ycaARGLXBM74Anj/rAjkcgAsf0FE7u3bohMEqBY3Kw\nm5I/TbTJFaji6NuT273Be+YM0uBWw97zW8M+gPdftkD98HC1T9xz438JjFTg93tH8/kbKbuD\n9QR8/nwUxinQ//xdOM5OOHY7Al3/odh2ZtJICRAgQIAAAQIECBBYtoACadmE/3979xpqWVnG\nARwds5qMTGkylSKKNCtsgi5WxEQ3KMu+VEYY1dCQRfah+hCBQp80CLpQHwqTqKlMUoMyCEYH\nApWm7EOY080bCY0iORVMTl76P7D2sM927X3W5cjM2fv3wp+117vWetdZv/PMnvPus/c6BiBA\ngAABAgQIECBAYFkETJCW5TvpOggQIECAAAECBAgQGC1ggjSa0AAECBAgQIAAAQIECCyLgAnS\nsnwnXQcBAgQIECBAgAABAqMFTJBGExqAAAECBAgQIECAAIFlETBBWpbvpOsgQIAAAQIECBAg\nQGC0gAnSaEIDECBAgAABAgQIECCwLAImSMvynXQdBAgQIECAAAECBAiMFjhh9AgGILA6AodX\n51Jd6TEooP6OwW/KCn1J6m+FvtnH4KWqv2Pwm+JLIkCAQAmc0oQGgaMhoP6OhrpzTgTU30TC\n8mgIqL+joe6cBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQePIFtjz5p3AGAptK4Kn5at+TvDS5M3k06dremx3r39QDXQ+wH4EZgb71\ntzXHvyp5Q3Jy8q/k4UQjMESgb/09Myc5L9meHEz+k2gEhgr0rb/p85yelbcm9yeHpjd4TIAA\nAQLjBS7MEI83qcdd28ezYx332a4H2I9Ai0Cf+vtwjj+QTOq1ljVBuiTRCAwR6FN/H8wJ6sWg\n6fq7OevbhpzYMQQi0Kf+psHqhcmqvarFmrBrBAgQILDBAr/KeH9LHkz2Jl3aBdnpcFJPziZI\nXcTsM0+ga/29LQM8ltyVfCF5eVITo/1J1eFFiUagr0DX+ntTBn4k+UtSLw5V/V2W1Cv31Ve/\nCdAI9BXoWn+z416ajnreq5ggzepYJ0CAwEiB5+f4ekvdN5LvJPVke04yr52aDT9Iar//NksT\npEBogwT61N9NOUPV3dtnzvTqpv/2mX6rBNYT6FN/P89gVX/vmhn0qqa/JvAagT4CfepvetzX\nZOV/Sb21rmrSBCkI2niB48cPYQQCSyPw0VxJ/Zv4ZfLj5qo+0SzbFjek80PJNcmuth30Eegh\n0LX+qkafkfwx2TMz/r6s/yk5K/EZ0xkcqwsFutZfDfKz5MtJPQdOtxublfoMp0agj0Cf+puM\nW8+Du5Nbk+81nTVJ0ggQIEBggwSOyzh3JfXWunp7SP1weV/yULI1aWvfSmd9KLRa3dihnpj9\nBqk0tL4CQ+qv7RxPS2d9WP6vbRv1EZgjsBH1V2Ncm9Tz4MvmnEc3gTaBofX37QxWn7t8YXJ5\nUrX3ukQjQIAAgQ0SeEvGqSfXb06NN3nC3TnVN++hCdI8Gf1dBMbW3+Qcl+VB1fEVkw5LAh0E\nxtRfvQ35S8ltSb1F+XOJRqCPwJD6q8/+1nPdx5oTTf6/NkHqI29fAgQIrCPww2yvJ9v6DMek\nnZ0H1ffbSceCpQnSAhyb1hUYW391gvcn9QPqn5OnJxqBrgJj6q9exa/nyUrdoOEViUagj0Df\n+jstgz+QXD91EhOkKQwPCRAgsBEC9fdj6u5LbR9svyX9sxOntnOaILWp6OsisBH195Gc6HDy\nj8TnP4KgdRYYW39n5kzPTXYlf0jqA/P1WCPQRWBI/dVn3w4kz5k6gQnSFIaHBAgQ2AiBT2aQ\nmgTVHzm8Zyb1/uba9t1kUTNBWqRj2yKBsfV3aQavGr0zecmiE9lGoEVgbP1ND1mfPaparImS\nRqCLQN/6+1QGrRr7QLJ1Kl9p+nc0ffW5Jo3AYAEFNJjOgUsk8LtcS/0l+J8m9cQ7285vOk7P\n8qHZjc16TZDqzk71/vt6otYIdBUYWn/1/P3V5JJkX/LupF5V1Qj0ERhaf/POcWs2vDZ5QXLv\nvJ30E2gE+tZf3SnxzR30zs4+dUdPjQABAgQGCJybY2pStHfBsd9v9vnMgn38BmkBjk1zBYbW\nX93q+6qkave6pF5J1Qj0FRhSfyflJHWXxPpBta3dnM6qy1PaNuojMCUwpP4+neO/3pKaaFXd\n/aTZti1LjQABAgQGCnwtx9WT6s4Fx+9o9rljwT4mSAtwbJorMLT+Ls6IVbfXJlvmjm4DgcUC\nQ+uvfhitG4Jsnxm+/khn9f9+pt8qgTaBofXXNpbPILWp6CNAgMAAgfp7Rw8mh5JnLTi+3spU\nr5jWD6TzfrVvgrQA0KZWgaH1d2pG+2dS9bgnuX5O6pV+jcA8gaH1V+O9MambMdyfXJHUbZo/\nnxxMHk5mJ07p0gisERhTf2sGalZMkNpU9BEgQGCAQN0WuX7IvLrDsV9cZ18TpA6IdlkjMLT+\nLmhqsWp3UZ695mxWCKwVGFp/k1Hqj2TvT6Zr8JasnzvZwZLAAoGx9Tc7tAnSrIh1AgQIECBA\ngACBoyJwRs5afz+ubtesESBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngMAmENiyCb5GXyIBAgQIEBgj8MocfF5yYnJgzECOJUCAAAECBAgQIECAwGYX2J8LeDy5Y7Nf\niK+fAAECBAgQIECAAAECYwRen4NrcrSvWe7IUiNAgAABAgQIECBAgMBKClyZq3402Z48llyd\naAQIECBAgAABAgQIEFg5gZNyxf9OftNc+a+zPJyc1qxbECBAgACBJwgc/4QeHQQIECBAYDkE\n3pfLqEnSNc3l7M7yKcnOZt2CAAECBAgQIECAAAECKyNQvzF6JJn8xujkPD6U3J14gTAIGgEC\nBAgQIECAAAECqyFwVi6zbs7wi5nL/VHTf/5Mv1UCBAgQIECAAAECBAgsrcDlubKaINXb7Kbb\nO7LSNnGa3sdjAgQIEFhhgeNW+NpdOgECBAgsp8AJuax7k+cl9yV1F7tJq7fWnZnUHe1elNyd\naAQIECBA4IjAliOPPCBAgAABAssh8M5cxq7k9uS2pCZJk/w9j+tzSGc0yz1ZagQIECBAgAAB\nAgQIEFhagetyZfU2uh1zrvDFzfYDWZ44Zx/dBAgQIECAAAECBAgQ2PQC23IF9beO7kkWvY18\nb7bXJOrCRCNAgAABAkcE3Ob0CIUHBAgQILAEAhflGupvHe1OagI0r13ZbLh43g76CRAgQIAA\nAQIECBAgsNkF6nNHNTE6Z50L2ZrtBzvuu85QNhMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCGwCgf8DOoFFNwVyZu8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(x ~ A, data = data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "subject-zoning",
   "metadata": {},
   "source": [
    "### 单因素方差分析"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceramic-significance",
   "metadata": {},
   "source": [
    "使用 aov 函数完成方差分析："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "surface-treatment",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "            Df   Sum Sq  Mean Sq F value Pr(>F)\n",
       "A            3 0.005846 0.001949   1.306    0.3\n",
       "Residuals   20 0.029850 0.001492               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfc <- aov(x~A, data=data)\n",
    "summary(dfc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "classical-mandate",
   "metadata": {},
   "source": [
    "从方差分析表中看到 p-value = 0.3 > 0.05，接收原假设 $H_0$，\n",
    "认为四种不同催化剂对产品的得到率无显著影响"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "skilled-treat",
   "metadata": {},
   "source": [
    "ref: http://www.datasoldier.net/archives/1315"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
